Hank Keeton

Alfred North Whitehead was first and foremost a mathematician. This project is an effort to examine one concept in his philosophical work, the concept of extensive connection, to find its roots in his mathematical background. After his doctoral work on Maxwell's electromagnetic theory, Whitehead attempted a unification of the new algebras of the middle nineteenth century in terms of generalized spaces. This led to work in the foundations of projective geometry that produced what this author calls the point-complexity intuition or the Axiom of Extension. From this intuition Whitehead draws the conclusion that points of space and instants of time are really extended entities, not the dimensionless units of classical mechanics. Combined with the insights of Special Relativity and the unification of time with space by Minkowski, Whitehead begins to develop an understanding of the foundation of scientific data in terms of units of spacetime he calls durations. ; His fundamental urge toward discovering foundational elements leads him into an effort with Bertrand Russell to find the structure and content of modern arithmetic in the axioms of logic. This work extends beyond the range of formal mathematics into the world of experience and Whitehead begins to develop a conceptual mechanism called the Method of Extensiveion. This method is the product of his analysis of logic, his point-complexity intuition and the axioms of identity and order from projective geometry, the latter constituting what this author calls the Axiom of Connection. The combination of the Method of Extensive Abstraction, the Axiom of Extension, and the Axiom of Connection reveals a fundamental aspect in the world of experience which Whitehead calls the passage of nature. This fundamental role of change in the world effectively injects a directionality into the basic units of spacetime. In fact, Whitehead discovers that spacetime concepts are really abstract derivatives from the more fundamental extended-directed-connected units of experience. ;The mature concept of extensive connection is the composite of the Axiom of Extension , the Axiom of Direction , and the Axiom of Connection . The function of this concept in experience as examined by Whitehead, is to reveal a topological structure in the world of change. This structure remains invariant with respect to particular elements in experience which are examined in his cosmological essay Process and Reality. It is the goal of this dissertation to follow the development of extensive connection as the Doctrine of Significance begins to emerge in Whitehead's mathematical work, and demonstrate its implications for that Doctrine as it becomes the Philosophy of Organism